Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee Effect

Yongli Cai, Caidi Zhao and Weiming Wang

Journal of Applied Mathematics, 2013, vol. 2013, 1-16

Abstract:

We investigate a diffusive Leslie-Gower predator-prey model with the additive Allee effect on prey subject to the zero-flux boundary conditions. Some results of solutions to this model and its corresponding steady-state problem are shown. More precisely, we give the stability of the positive constant steady-state solution, the refined a priori estimates of positive solution, and the nonexistence and existence of the positive nonconstant solutions. We carry out the analytical study for two-dimensional system in detail and find out the certain conditions for Turing instability. Furthermore, we perform numerical simulations and show that the model exhibits a transition from stripe-spot mixtures growth to isolated spots and also to stripes. These results show that the impact of the Allee effect essentially increases the model spatiotemporal complexity.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:535746

DOI: 10.1155/2013/535746

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